Division

Quote from start of section:
(Division is) an operation that is even less frequent and even more quirky (than Multiplication). It even offers an opportunity to perform a mathematically invalid operation: dividing by 0
Dividend = Qotent X Rivison + Remainder

              239   (Quotient)
              ------
(Divisor) 123|29481  (Dividend)
              246
               488
	       369
	       1191
	       1107
	         84 (Remainder)

Algorithm
- Find how many times the Divisor goes into the first part of the Dividend
- Record that as part of the Quotient
- Subtract from Dividend, repeat
- Until the remainder is less than the divisor
Again in binary, division is simpler.
- Either subtract, and add a 1 to the quotient
- Or Add a 0 to the quotient.
- In either case, shift the divisor right and the quotient left
- See picture page 266
  - Set the divisor left hand side of the divisor register.
  - Set the Quotient to 0
  - Set the Remainder register to the dividend.
- Until we have looped 33 times
  - Subtract the Divisor from the remainder register.
  - If the result is positive, add 1 to the quotient register
  - Otherwise restore remainder (add divisor back in), add 0 to quotient register
  - In any case, shift divisor right, and quotient left.
- Again, 64 bit registers and a bunch of shifting.
- In the second version, page 269
  - Store the Dividend in the Remainder Register
  - Shift the remainder register to the left
- Final version, on page 271 is much the same as the multiplier.
  - Notice that we can store the quotient in the bottom of the remainder register
  - We might have to shift the bottom half right at the end.
Signed division is a problem.
- If the signs are both positive, the results are positive.
- The modulus of the remainder gives us a problem
- 5 % 3 = 2, or -1
- We need to pick a convention, and make the sign right.
In MPIS
- div $r1, $r2
- Quotient is in $lo
- Remainder is in $hi
- divu $r1, $r2
- mfhi $r1, move from hi to r1
- mflo $r1, move from low to r1